Mini-Lab 3 : Design Your Own Physics Problem!
Mini-Lab 3 : Design Your Own Physics Problem!
As we get closer to the first exam, it’s time to get serious about problem solving! Remember that 60% (+10% Bonus!) of the first exam will be problems similar to the homework, testing problem solving skills developed throughout the semester. As always, the best way to prepare for this is practice, practice, practice.
One way to get better at solving problems is to create your own problems to solve. Although this may sound counterintuitive, creating a good physics problem is a creative task in its own right, and as you work through all the parts necessary to develop a well-posed physics problem, you may be able to get a “big-picture” view of how these problems work and are solved.
In this mini-lab, I will ask you to create and solve your own physics problems from the chapters we have covered over the semester. These problems must be :
Well-posed (Have a definite solution).
Unique (Have enough information given to arrive at a single numerical answer).
Solvable using only the material covered in class so far.
Include an image or visual aid if applicable.
Once you’ve created your own problem, you’ll be asked to provide a solution to one of your classmates problems! To aid you in your first time problem creation, I’ve included an example of how this might work below.
Example : Sonic & Tails
Usually creating a good physics problem has several steps.
Pick a real world or imagined scenario which involves a simple type of motion we’ve studied. For my example, I’ve chosen a race between Sonic and Tails.
Decide on what simplifications or assumptions you will need in order to design your problem. This might include answering questions like : Can I treat the objects as particles in describing the motion, or are their sizes and dimensions important? Are the objects accelerating? Is this acceleration constant, or do I want to make it vary? Are the objects moving in a straight line, or along a curved path? For my example, I’ll choose a simple 1D race with Sonic moving at a constant speed, and Tails moving with a constant acceleration.
Write down the relevant physics equations based on the simple model and assumptions you have in mind. For example, with Sonic and Tails moving in a straight line, these would be the 1D kinematic and uniform motion equations for Sonic and Tails :
x s = x 0 s + v 0 s t
x t = x 0 t + v 0 t t + 1 2 a t t 2
v t = v 0 t + a t t
Writing down the equations allows you to work backward and see what variables you will need to specify when you ask the question. For example, with the three equations for the problem above, I can count the number of variables relevant to the problem, in this case 9. This will be important in deciding how many of these you will need to specify when you write your problem. Remember, in order to solve a problem you need to have
# of equations = # of unknowns
Decide which of these variables you are going to ask about, i.e., which are going to be your unknowns. For my example, since I have three equations, I can ask for at most 3 of these, and the rest I will need to specify either directly or indirectly in the problem. For my problem, I’ve decided to ask for the time it takes Tails to catch up to Sonic, assuming Sonic has a head start and is moving with a constant speed. This means I will be asking for the variable t. Remember, you don’t always need to specify every variable in the problem, as some of these can chosen by the student solving the problem. For example, by choosing your axes, you can always specify the initial position of either Sonic or Tails to be zero, but you might need to specify how far away from each other they are.
Check if there are any additional relations or equations given by what you’re asking for. For example, since I’m asking for the time at which they meet, their positions will be equal at this time, giving the further equation
x s = x t
, further reducing the number of possible unknowns.
Put it all together and ask your question! I’ve decided on the following :
“Sonic and Tails race along a straight track towards the finish line. Sonic is initially 25 m ahead of tails, moving with a uniform speed of 100 m/s. Tails, who is moving at 75 m/s, decides to speed up to try and pass Sonic, accelerating uniformly at 5.7 m/s. How long does it take to for Tails to catch up to Sonic?”
Check the number of unknowns. For my problem, assuming the student were to set the initial position of Tails to be zero and given that
x s = x t
when they meet, this leaves 7 possible unknowns. In the problem statement I’ve given four pieces of additional information, leaving (7-4) = 3 unspecified variables, as required.
Most importantly, once you’ve asked your question, see if it makes sense! Try to solve your own question and make sure you’ve given enough information. Think about how you could modify the question and ask for other variables. This will help you on the exam when slight modifications of HW or class problems show up!
Submission Details
To receive full credit for this assignment you will need to :
(10 pts) Reply to the discussion post with your own original problem, satisfying the conditions above. Include any necessary images or supplementary materials!
(10 pts) Reply to one of your classmates posts with your own solution to their created problem. This may be an image file similar to what is submitted on the exams.
